Modelling of thermal regimes in the air cooling channel of the titanium reduction apparatus

Abstract

Numerical modeling of thermophysical processes in the air cooling channel of titanium sponge reduction apparatus is performed. The cooling channel is an area bounded by a retort filled with liquid magnesium and the apparatus wall, on which heating elements are mounted. Air flows inside the channel, cooling the retort. A mathematical model is constructed based on unsteady Navier-Stokes equations in axisymmetric formulation using a k-ω SST turbulence model. The model takes into account the radiation heat transfer between the retort and reactor walls. Four variants of thermal boundary conditions are considered. The aim of this work is to create a mathematical model of conjugate heat transfer in an air channel. Based on this model, the temperature conditions of the retort wall are calculated and the profiles of the heat transfer coefficient along the retort wall for a wide interval of air flow rates are obtained. It is shown that temperature distributions along the retort are heterogeneous and strongly depend both on external boundary conditions and on the cooling intensity. Heat transfer coefficient distributions from its outer wall for different retort heating conditions are plotted and an empirical formula for calculating the profile of this coefficient is proposed.